Question

The tension in piano wire is $10 \,N$.What should be the tension in the wire to produce a note of double the frequency?

• A. 40 N
• B. 5 N
• C. 80 N
• D. 20 N.

Answer 1

Answer: (A)

40 N

Answer 2

Given: Initial tension in the piano wire $\left(T_{1}\right)$ $=10\, N ;$ Initial frequency of note $\left(n_{1}\right)=n$ and final frequency of the note $\left(n_{2}\right)=2 n .$ We know that frequency $(n)=\frac{1}{2 \pi} \sqrt{\frac{T}{m}} \propto \sqrt{T} .$ Therefore $\frac{n_{1}}{n_{2}}=\sqrt{\frac{T_{1}}{T_{2}}}$ or $\left(\frac{n}{2 n}\right)^{2}=\frac{10}{T_{2}} .$ Therefore final tension $\frac{1}{4}=\frac{10}{T_{2}}$ or $T_{2}$ $=10 \times 4=40\, N$